PSI - Issue 12

Gabriele Cricrì et al. / Procedia Structural Integrity 12 (2018) 492–498 Gabriele Cricrì / Structural Integrity Procedia 00 (2018) 000 – 000

496

5

displacement at the central loading point. To the aim obtaining a sufficiently detailed-in-time solution, since the cohesive elements are affected by material nonlinearity, the external load was split into 300 sub-steps and the solution for each of them is calculated using a Newton-Raphson scheme. The analyses were performed with the ANSYS code. The overall response of the simulation is shown in the following figures. In particular, in Figs. 3-4 the displacements and stresses in the x -direction of the adherends are shown, as resulting from the simulation at an intermediate step of the loading process.

Fig. 3. FE virtual test output – x displacements

Fig. 4. FE virtual test output – x normal stress

Figure 5 shows the results of the simulation relevant to the cohesive law identification. Note that the load curve P(  ) is strictly increasing, as previously written. In this regard, it is observed that the sequence of the load curves resulting from the ENF, 4ENF and TNF test simulations has increasing stability properties. This characteristic is attributed to the fact that the total bending moment applied at the beginning of the glued zone (i.e. at point x a ) is, respectively, for the three tests, increasing, constant and decreasing in the direction of the crack length increase (i.e. the direction of increasing x ). A similar explanation to justify the stability of the ONF test is also invoked in Wang and Vu-Khanh (1996). In order to evaluate the correctness and efficiency of the proposed TNF test, the data obtained from the virtual test were used to calculate Q(v) . The calculation has been performed by means of the iterative algorithm described in the previous section; subsequently, the interface shear stress  (v) has been calculated by numerical differentiation. It is noted that the entire identification process was performed using a simple spreadsheet. As shown in Figure 6, the result is practically indistinguishable from the integral of the cohesive law (8), imposed in the FE model and reported below in closed form: ( ) = ∫ ( ) 0 = (1 − −( ) 2 ) (9)